The contents of this paper
belong to the general algebraic theory of those algebras which are studied in
connection with algebraic logic. The main results, Theorems 1 and 2, give sufficient
conditions for the amalgamation and the embedding property to fail in a
class of Boolean algebras with operators. As a corollary, for 1 < α < ω, the
amalgamation property fails in the class of all (representable) cylindric algebras of
dimension α and in the class of all (representable) polyadic (equality) algebras
of dimension α. Thus, there are finitely axiomatizable equational classes
of Boolean algebras with operators for which the amalgamation property
fails.
